Calcium Oscillations -- Oscillations by the p53-Mdm2 Feedback Loop -- cAMP Oscillations during Aggregation of Dictyostelium -- Min Oscillation in Bacteria -- Development on Time -- Oscillatory Expression of Hes Family Transcription Factors: Insights from Mathematical Modelling -- Reverse Engineering Models of Cell Cycle Regulation -- Mitochondrial Oscillations in Physiology and Pathophysiology -- Respiratory Oscillations in Yeasts -- Stochastic Phase Oscillator Models for Circadian Clocks. Living systemsare fundamentally dynamic and adaptive, relying on a constant throughput of energy. They are also, by definition, self-sustaining over the full range oflength and time scales (from sub-cellular structures to species considered as a whole). This characteristic combinationofconstant adaptive flux and emergent persistence requires that the propertiesofall living systems must, at some level, be cyclical. Consequently, oscillatory dynamics, in which system properties rise and fall in a regular rhythmic fashion, are a central featureofa wide rangeofbiological processes. The scale of biological oscillations covers enormous ranges, from the sub-cellular to the population level, and from milliseconds to years. While the existenceofanumberofbiologicaloscillations-such as the regular beating of the human heart or the life-cycle ofa unicellular organism-is widely appreciated, therearemanyoscillatoryphenomenathataremuchlessobvious,albeit no less important. Since oscillations reflect periodic quantitative changes in system properties,theirdetectionandcharacterisationreliesonthequantitativemeasurement ofa systemoveranextendedperiod. Untilrecently, suchmeasurements were difficult toobtainatcellularorsub-cellularresolution, andrelatively few cellularoscillations had been described. However, recent methodological advances have revealed that oscillatory phenomena are as widespread in cells as they are at larger scales. The chapters inthis bookprovide an introduction to arangeofbothwellknown and less familiar cellular oscillations and serve to illustrate the striking richness of cellular dynamics. The contributions focus particularly on elucidating the basic mechanisms that underlie these oscillations. The essentially quantitative nature of oscillations has longmade theman attractive areaofstudyfor theoretical biologists (see, for example, refs. 1-3), and the application ofcomplementary modelling and experimental approachescanyieldinsightsintooscillatorydynamics thatgobeyond those that can be obtained by either in isolation. The benefits ofthis synergy are reflected in the contributions appearing in this book.